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Multiply-add speed is important

Some DSP processes require extremely large numbers of multiply-add operations. In order to perform DSP in real time, the equipment used to performthe arithmetic must be extremely fast. That is where the special DSP chips, (which are designed to perform multiply-add operations at an extremely high rate of speed) earn their keep.

The net area under the curve

If you plot a time series as a curve on a graph, as shown in Figure 3 , the sum of the values that make up the time series is an estimate of the net areaunder the curve.

(Assuming that the horizontal axis represents a value of zero, the sample values above the axis contribute a positive value to the net area and thesample values below the curve contribute a negative value to the net area. In the case of Figure 3 , I attempted to come up with a set of sample values that would produce a net area of zero. In other words, the area above thehorizontal axis was intended to perfectly balance the area below the horizontal axis.)
Figure 3. Plot of values in a time series.
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A periodic example

A periodic time series is one in which a set of sample values repeats over time, provided that you record enough samples to include one or more periods. Figure 4 shows a plot of a periodic time series. You can see that the same set of values repeats as you move from left to right on the curve plotted in Figure 4 .

Figure 4. Area under a periodic curve.
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The sum of two curves

Periodic curves can often be viewed as the sum of two curves. One of the curves is the periodic component having a zero net area under the curve whenmeasured across an even number of cycles. The other component is a constant bias offset that is added to every value of the periodic curve.

Each of the solid dark blobs in Figure 4 is a sample value. The horizontal line represents a sample value of zero. (The empty circle is the sample value half way through the sampling interval. The only reason it is different isto mark the mid point.)

The net area under the curve

What is the net area under the curve in Figure 4 ? Can you examine the curve and come up with a good estimate. As it turns out, the net area under the curvein Figure 4 is very close to zero (at least it is as close to zero as I was able to draw it) .

Now take a look at Figure 5 . What is the net area under the curve in Figure 5 ?

Figure 5. Area under a periodic curve with an offset.
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Compare Figure 5 To Figure 4

Each of these curves describes the same periodic shape (although Figure 4 has a larger peak-to-peak amplitude, meaning simply that every value in Figure 4 has been multiplied by the same scale factor) .

However, the curve in Figure 5 is riding up on a positive bias, while the curve in Figure 4 is centered about the horizontal axis. While the net area under the curve in Figure 4 is near zero, the net area under the curve in Figure 5 is a non-zero positive value.

The curve in Figure 5 can be considered to consist of the sum of two parts. One part is a straight horizontal line on the positive side of the horizontalaxis. The other part is the periodic curve from Figure 4 , added to that positive bias.

Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
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Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
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Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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